Need help with integrals from Landau-Lifshitz vol. 1 problems

JevKus

Hi!

I'm new to this forum and forums in general, so please be forgiving.

I am currently going through problems in Landau-Lifshitz's vol. 1 (Mechanics) and encountered two integrals I can't solve. The physical basis of the problem is crystal clear, but I can't do the final computation. The integrals are from problem 2 (b,c) par. 11. Mathematica spits out correct answers, so I won't post the full problem and will only post integrals I'm having problems with.

The first one is:
[itex]\int_{1}^{a}\frac{dz}{z \sqrt{z^{2} - 1}\sqrt{a^{2} - z^{2}}}[/itex];

here [itex]z[/itex] and [itex]a>1[/itex] are assumed to be real.

The other one is:
[itex]\int_{0}^{a}\frac{dz}{(1 + z^{2})\sqrt{a^{2} - z^{2}}}[/itex].

[itex]z[/itex] and [itex]a[/itex] are also assumed to be real.

Thank you!